The conventional wisdom holds that chance operations abolish "glue" (Henry Cowell's term, but often invoked by Cage).  That idea rests on presuming that statistical independence governs how  the operations place musical events within the music framework.  Well, not here.

As x and y coordinatize the Euclidean plane, time and pitch coordinatize musical space as constructed say on a piano roll.  But there's a difference: the plane enjoys rotational symmetry, but its far from clear how one would even compare the magnitude of a time duration with musical interval.

Take a circle and randomly choose 41 chords (meaning, sorry, line segments that connect two points on the circumference).  That makes 820 pairs of chords, but only above one third of the pairs will intersect (meaning, inside the circle).  Those roughly 270 points of intersection, plotted on a virtual piano roll, become the notes of a variation.  The piece consists of 10 variations.  Each note/point sits on two lines, so each line will contain an average of about 13 notes.  This is the emergent clue.  Depending on the slope of the line segment, it will sound as a chord, a broken chord, an arpeggio, a line slowly ascending or descending, or even a pedal tone.  Of course the points/notes on a line don't sit evenly spaced - their position gets determined by the random dispositions of the other chords.  But every note is overdetermined -- by design it sits on two lines and thus helps describe two different musical figures.

Empirically, the 88 note space of the piano (so 352 distinct pitches by the use of eighth-tones) feels like one minute.  Too much faster and the emergent shapes get compressed into illegibility, too much slower and the notes get unglued by the strain on short-term memory.

The accompanying graphic explores a similar construction, but in the visual realm.

Time-Space-Circle-Line-Point #7, for four pianos tuned in eighth tones

I am a British composer, who has studied composition privately with British composer Peter Nickol https://www.impulse-music.co.uk/peternickol/ (although I am largely self-taught). I have also studied piano (privately) with concert pianist Ekaterina Shetliffe. 
My music contains elements of impressionism, and musical modernism; I have also explored 12-tone composition.
For several years now, I have been developing my own composition technique, which focuses on the liminal area between stochastic and spectral music, which I intend to use in my future compositions.

Composers who have influenced me include Schumann, Chopin, Schoenberg, and Ligeti; however my formative musical inspiration is the music of Debussy.

*My music and poetry is copyrighted.*

Composer, mathematician, visual artist. 
Seeks collaboration with performers and choreographers.

Please don't spam this account!

Instrumental Dark Folk with violin and acoustic guitar from Dresden, Germany.

To all concerned: 
I am announcing publication of my new book, NOW AVAILABLE:
https://www.routledge.com/Maqam-Melodies-Pitches-Patterns-and-Developments-of-Music-in-the-Middle-East-and-other-Microtonal-Writings/Thoegersen/p/book/9789815129052
My book, Polytempic Polymicrotonal Music, is available on Amazon. 
https://www.routledge.com/Polytempic-Polymicrotonal-Music-The-Road-Less-Traveled/Thoegersen/p/book/9789814968294

I have a new album out through Magic&Unique Group Records on Spotify and other digital streaming platforms:
https://open.spotify.com/album/5qWHmcvyAemvVn2TJH1bio?si=OD5TmPptQ-ypr8WOI0EZKA&nd=1

https://whitecentipedenoise.com/products/peter-thoegersen-facebook-cantos-cdr-flea
My CD via Flea label has been out since April, 2021, featuring the wonderful Lore Lixenberg singing over my microtonal piano accompaniment
Hope you enjoy it!

https://www.newworldrecords.org/collections/vendors?q=Peter%20Thoegersen

From the liner notes on my CD now available on AMAZON and New World Records:
"The author of these notes has spent his life explaining radical music, and the music on this disc may be the most radical I've ever written about. Peter Thoegersen (b. 1967) is not yet a name known to the music world; not for any lack of connection to other famous musicians, but because he came to composition late, and because his artistic aims are so broad and complex that they have taken years to evolve. His aesthetic is well defined, and he is upfront about having a name for it: "Polytempic Polymicrotonal Music." That means he has musical layers simultaneously moving in different tempos, plus, even more radically, that he has different microtonal scales playing at the same time. Few composers have aimed at such fervent and heterogeneous multidimensionality. And yet, while Thoegersen's music can seem overwhelming at first, running through it is a level of charm and simplicity that belies the initial impression.

In total, these three pieces emphasize a particular side of Thoegersen's output. The image his music creates of ornately mathematical structures filled with intuitively friendly melodies maps on to the personality of the man himself: outspoken and acerbically ruthless in his musical opinions, Thoegersen is also marked by a jolly sense of humor and an inexhaustible love of cats and other animals that make him ultimately less imposing and more personable than he might seem at first. The same can be said for his music. And by going further than anyone else has gone in terms of this particularly American concept of fusing the polytempic with the polymicrotonal - extending and combining the conceptual worlds of Ives, Cowell, Nancarrow, Partch, Carter, even Frank Zappa and many others - he has created a special place for himself within American music."                                                             

-Kyle Gann (from the liner notes)

This is my Soundcloud.

https://www.beatport.com/release/keine-zeit/2167806
http://flo-huth.de
https://www.instagram.com/elektrosmogma

collaborations, shared projects, ideas ..

http://marcolucchi.bandcamp.com/

https://musichevirtuali.blogspot.com/

www.musichevirtuali.org

https://twitter.com/musichevirtuali

https://www.facebook.com/pages/orchestra-eclettica-e-sincretista/111790807863?fref=ts

"I'm a mellow artist, ageing 69. I love and release eclectic music, from post-classical to drone. My fave instrument is the Mellotron."

Così, sinteticamente, di solito mi presento.

In genere compongo musica partendo dal suono delle tastiere, ma il mio vero strumento è il registratore.

O i software di registrazione.

"I was made for loving and making recorded music."

Confido da sempre nel potere evocativo e orfico della musica, nella sua capacità di riconsegnarci a mondi più veri e più giusti, più belli di quelli in cui di solito viviamo.

"Ich bin ein kosmische Kurier"

I'm using these tools: Mellotron micro, Waldorf Blofeld synthesizer, Behringer Crave, IK Multimedia Uno synth, Roland Juno synth, Volca keys, Casio digital piano, micropiano Korg, Manetron (iPad app), iTampura (iPad app), Eko 11 (...) string acoustic guitar, electric violin, Orla analogic expander, tenor, treble and descant recorders, soprano and tenor tin whistle, Akai, Roland, Alesis and Arturia controllers, upright piano, Squier 3/4 electric guitar, melodica, Bubble Harp (iPad app), Schoenhut toy harp, soprano ukulele, Eko acoustic guitar, Peavey Composer acoustic guitar, Kurzweill micropiano, Boss and JamMan loop stations , Behringher multi-fx, Olympus portable digital recorder, Phonic, Behringer and Yamaha mixers, Audacity, Paulstretch, various players and plug-ins .. (that's all, folks, I think ..)

latest releases:

https://whitelabrecs.bandcamp.com/album/the-book-of-dreams
https://chitrarecords.bandcamp.com/album/lieder-ohne-worte 
https://ambientologist.bandcamp.com/album/suggestiva
https://ambientologist.bandcamp.com/album/venusia
https://hibernate.bandcamp.com/album/as-riddled-as-the-tide

for further works please go to my bandcamp page
https://marcolucchi.bandcamp.com/

and to 
http://webbedhandrecords.com/
http://www.laverna.net/home/
https://silentflow.org/

iTunes and Spotify as well ..
feed and share ..
https://open.spotify.com/artist/1TRilVaDaQw0ksGqU5tuCh?si=zXD-0xFWS-2yrUs542SH9A

SoundCloud è la piattaforma musicale che preferisco perché è soprattutto il regno degli ‘amateurs’, di quelli che fanno musica per sé e per gli amici .. come quando da ragazzi si condividevano con gli altri le invenzioni e le creazioni .. io sostanzialmente sono rimasto lì e così .. non sempre, ovviamente, ma spesso ci trovo delle cose che valgono altrettanto - se non di più - rispetto a quelle più affermate e conosciute

Time-Space-Circle-Line-Point #7, for four pianos tuned in eighth tones

David Victor Feldman